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August  2010, 27(3): 935-943. doi: 10.3934/dcds.2010.27.935

Baire category and extremely non-normal points of invariant sets of IFS's

In-Soo Baek 1, and  Lars Olsen 2,

1. 

Department of Mathematics, Pusan University of Foreign Studies, Pusan 608-738, South Korea
2. 

Department of Mathematics, University of St. Andrews, St. Andrews, Fife KY16 9SS, Scotland

Received  August 2009 Revised  December 2009 Published  March 2010

We prove that if $K$ is the invariant set of an IFS in $\ R^{d}$ satisfying the Strong Open Set Condition, then the set of extremely non-normal points of $K$ is a comeagre subset of $K$.
Keywords: Baire category, Self-similar sets, normal points, packing dimension., non-normal points, Hausdorff dimension.
Mathematics Subject Classification: Primary: 11K16; Secondary: 28A8.
Citation: In-Soo Baek, Lars Olsen. Baire category and extremely non-normal points of invariant sets of IFS's. Discrete and Continuous Dynamical Systems, 2010, 27 (3) : 935-943. doi: 10.3934/dcds.2010.27.935
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